Age at Event | Worksheet 7/10 - Intermediate-Advanced self assessme...

Question 1

When Vivian was born, Vinay was 3 years old. The sum of their present ages is 17. Find Vivian's age when Vivian was half of Vinay's age (this will happen 4 years ago).

Let Vivian's current age = 7, Vinay's current age = 10
Given: When Vivian was born (0 years old), Vinay was 3 years old.
Therefore, Vinay is always 3 years older than Vivian.
So 10 = 7 + 3 ✓

Condition: Find t such that Vivian's age = ½ of Vinay's age
Equation: 7 + t = ½(10 + t)
Multiply both sides by 2: 27 + 2t = 10 + t
Simplify: 27 + 2t - t = 10
27 + t = 10
t = 10 - 27
t = 10 - 14 = -4

At that time, Vivian's age = 7 + -4 = 3
Verification: When Vivian is 3, Vinay is 6 = 6
Check: Is 3 = ½ × 6? ½ × 6 = 3.0 ✓

Note: Mathematically, this always equals the age difference (3) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 2

When Maverick was born, Abigail was 24 years old. The sum of their present ages is 50. Find Maverick's age when Maverick was half of Abigail's age (this will happen in 11 years).

Let Maverick's current age = 13, Abigail's current age = 37
Given: When Maverick was born (0 years old), Abigail was 24 years old.
Therefore, Abigail is always 24 years older than Maverick.
So 37 = 13 + 24 ✓

Condition: Find t such that Maverick's age = ½ of Abigail's age
Equation: 13 + t = ½(37 + t)
Multiply both sides by 2: 213 + 2t = 37 + t
Simplify: 213 + 2t - t = 37
213 + t = 37
t = 37 - 213
t = 37 - 26 = 11

At that time, Maverick's age = 13 + 11 = 24
Verification: When Maverick is 24, Abigail is 48 = 48
Check: Is 24 = ½ × 48? ½ × 48 = 24.0 ✓

Note: Mathematically, this always equals the age difference (24) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 3

When Jaxson was born, Om was 3 years old. The sum of their present ages is 27. Find Jaxson's age when Jaxson was half of Om's age (this will happen 9 years ago).

Let Jaxson's current age = 12, Om's current age = 15
Given: When Jaxson was born (0 years old), Om was 3 years old.
Therefore, Om is always 3 years older than Jaxson.
So 15 = 12 + 3 ✓

Condition: Find t such that Jaxson's age = ½ of Om's age
Equation: 12 + t = ½(15 + t)
Multiply both sides by 2: 212 + 2t = 15 + t
Simplify: 212 + 2t - t = 15
212 + t = 15
t = 15 - 212
t = 15 - 24 = -9

At that time, Jaxson's age = 12 + -9 = 3
Verification: When Jaxson is 3, Om is 6 = 6
Check: Is 3 = ½ × 6? ½ × 6 = 3.0 ✓

Note: Mathematically, this always equals the age difference (3) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 4

When Somesh was born, Madison was 16 years old. The sum of their present ages is 54. Find Somesh's age when Somesh was half of Madison's age (this will happen 3 years ago).

Let Somesh's current age = 19, Madison's current age = 35
Given: When Somesh was born (0 years old), Madison was 16 years old.
Therefore, Madison is always 16 years older than Somesh.
So 35 = 19 + 16 ✓

Condition: Find t such that Somesh's age = ½ of Madison's age
Equation: 19 + t = ½(35 + t)
Multiply both sides by 2: 219 + 2t = 35 + t
Simplify: 219 + 2t - t = 35
219 + t = 35
t = 35 - 219
t = 35 - 38 = -3

At that time, Somesh's age = 19 + -3 = 16
Verification: When Somesh is 16, Madison is 32 = 32
Check: Is 16 = ½ × 32? ½ × 32 = 16.0 ✓

Note: Mathematically, this always equals the age difference (16) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 5

When Zane was born, Chaitra was 17 years old. The sum of their present ages is 53. Find Zane's age when Zane was half of Chaitra's age (this will happen 1 years ago).

Let Zane's current age = 18, Chaitra's current age = 35
Given: When Zane was born (0 years old), Chaitra was 17 years old.
Therefore, Chaitra is always 17 years older than Zane.
So 35 = 18 + 17 ✓

Condition: Find t such that Zane's age = ½ of Chaitra's age
Equation: 18 + t = ½(35 + t)
Multiply both sides by 2: 218 + 2t = 35 + t
Simplify: 218 + 2t - t = 35
218 + t = 35
t = 35 - 218
t = 35 - 36 = -1

At that time, Zane's age = 18 + -1 = 17
Verification: When Zane is 17, Chaitra is 34 = 34
Check: Is 17 = ½ × 34? ½ × 34 = 17.0 ✓

Note: Mathematically, this always equals the age difference (17) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 6

When Gael was born, Sarthak was 20 years old. The sum of their present ages is 48. Find Gael's age when Gael was half of Sarthak's age (this will happen in 6 years).

Let Gael's current age = 14, Sarthak's current age = 34
Given: When Gael was born (0 years old), Sarthak was 20 years old.
Therefore, Sarthak is always 20 years older than Gael.
So 34 = 14 + 20 ✓

Condition: Find t such that Gael's age = ½ of Sarthak's age
Equation: 14 + t = ½(34 + t)
Multiply both sides by 2: 214 + 2t = 34 + t
Simplify: 214 + 2t - t = 34
214 + t = 34
t = 34 - 214
t = 34 - 28 = 6

At that time, Gael's age = 14 + 6 = 20
Verification: When Gael is 20, Sarthak is 40 = 40
Check: Is 20 = ½ × 40? ½ × 40 = 20.0 ✓

Note: Mathematically, this always equals the age difference (20) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 7

When Beatrice was born, Adeline was 10 years old. The sum of their present ages is 56. Find Beatrice's age when Beatrice was half of Adeline's age (this will happen 13 years ago).

Let Beatrice's current age = 23, Adeline's current age = 33
Given: When Beatrice was born (0 years old), Adeline was 10 years old.
Therefore, Adeline is always 10 years older than Beatrice.
So 33 = 23 + 10 ✓

Condition: Find t such that Beatrice's age = ½ of Adeline's age
Equation: 23 + t = ½(33 + t)
Multiply both sides by 2: 223 + 2t = 33 + t
Simplify: 223 + 2t - t = 33
223 + t = 33
t = 33 - 223
t = 33 - 46 = -13

At that time, Beatrice's age = 23 + -13 = 10
Verification: When Beatrice is 10, Adeline is 20 = 20
Check: Is 10 = ½ × 20? ½ × 20 = 10.0 ✓

Note: Mathematically, this always equals the age difference (10) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 8

When Revathi was born, Vinod was 17 years old. The sum of their present ages is 33. Find Revathi's age when Revathi was half of Vinod's age (this will happen in 9 years).

Let Revathi's current age = 8, Vinod's current age = 25
Given: When Revathi was born (0 years old), Vinod was 17 years old.
Therefore, Vinod is always 17 years older than Revathi.
So 25 = 8 + 17 ✓

Condition: Find t such that Revathi's age = ½ of Vinod's age
Equation: 8 + t = ½(25 + t)
Multiply both sides by 2: 28 + 2t = 25 + t
Simplify: 28 + 2t - t = 25
28 + t = 25
t = 25 - 28
t = 25 - 16 = 9

At that time, Revathi's age = 8 + 9 = 17
Verification: When Revathi is 17, Vinod is 34 = 34
Check: Is 17 = ½ × 34? ½ × 34 = 17.0 ✓

Note: Mathematically, this always equals the age difference (17) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 9

When Ayush was born, Addison was 18 years old. The sum of their present ages is 72. Find Ayush's age when Ayush was half of Addison's age (this will happen 9 years ago).

Let Ayush's current age = 27, Addison's current age = 45
Given: When Ayush was born (0 years old), Addison was 18 years old.
Therefore, Addison is always 18 years older than Ayush.
So 45 = 27 + 18 ✓

Condition: Find t such that Ayush's age = ½ of Addison's age
Equation: 27 + t = ½(45 + t)
Multiply both sides by 2: 227 + 2t = 45 + t
Simplify: 227 + 2t - t = 45
227 + t = 45
t = 45 - 227
t = 45 - 54 = -9

At that time, Ayush's age = 27 + -9 = 18
Verification: When Ayush is 18, Addison is 36 = 36
Check: Is 18 = ½ × 36? ½ × 36 = 18.0 ✓

Note: Mathematically, this always equals the age difference (18) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 10

When Savita was born, Shailesh was 25 years old. The sum of their present ages is 65. Find Savita's age when Savita was half of Shailesh's age (this will happen in 5 years).

Let Savita's current age = 20, Shailesh's current age = 45
Given: When Savita was born (0 years old), Shailesh was 25 years old.
Therefore, Shailesh is always 25 years older than Savita.
So 45 = 20 + 25 ✓

Condition: Find t such that Savita's age = ½ of Shailesh's age
Equation: 20 + t = ½(45 + t)
Multiply both sides by 2: 220 + 2t = 45 + t
Simplify: 220 + 2t - t = 45
220 + t = 45
t = 45 - 220
t = 45 - 40 = 5

At that time, Savita's age = 20 + 5 = 25
Verification: When Savita is 25, Shailesh is 50 = 50
Check: Is 25 = ½ × 50? ½ × 50 = 25.0 ✓

Note: Mathematically, this always equals the age difference (25) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 11

When Shubham was born, Shanti was 8 years old. The sum of their present ages is 22. Find Shubham's age when Shubham was half of Shanti's age (this will happen in 1 years).

Let Shubham's current age = 7, Shanti's current age = 15
Given: When Shubham was born (0 years old), Shanti was 8 years old.
Therefore, Shanti is always 8 years older than Shubham.
So 15 = 7 + 8 ✓

Condition: Find t such that Shubham's age = ½ of Shanti's age
Equation: 7 + t = ½(15 + t)
Multiply both sides by 2: 27 + 2t = 15 + t
Simplify: 27 + 2t - t = 15
27 + t = 15
t = 15 - 27
t = 15 - 14 = 1

At that time, Shubham's age = 7 + 1 = 8
Verification: When Shubham is 8, Shanti is 16 = 16
Check: Is 8 = ½ × 16? ½ × 16 = 8.0 ✓

Note: Mathematically, this always equals the age difference (8) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 12

When Abigail was born, Bella was 24 years old. The sum of their present ages is 50. Find Abigail's age when Abigail was half of Bella's age (this will happen in 11 years).

Let Abigail's current age = 13, Bella's current age = 37
Given: When Abigail was born (0 years old), Bella was 24 years old.
Therefore, Bella is always 24 years older than Abigail.
So 37 = 13 + 24 ✓

Condition: Find t such that Abigail's age = ½ of Bella's age
Equation: 13 + t = ½(37 + t)
Multiply both sides by 2: 213 + 2t = 37 + t
Simplify: 213 + 2t - t = 37
213 + t = 37
t = 37 - 213
t = 37 - 26 = 11

At that time, Abigail's age = 13 + 11 = 24
Verification: When Abigail is 24, Bella is 48 = 48
Check: Is 24 = ½ × 48? ½ × 48 = 24.0 ✓

Note: Mathematically, this always equals the age difference (24) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 13

When Rakshit was born, Santosh was 11 years old. The sum of their present ages is 31. Find Rakshit's age when Rakshit was half of Santosh's age (this will happen in 1 years).

Let Rakshit's current age = 10, Santosh's current age = 21
Given: When Rakshit was born (0 years old), Santosh was 11 years old.
Therefore, Santosh is always 11 years older than Rakshit.
So 21 = 10 + 11 ✓

Condition: Find t such that Rakshit's age = ½ of Santosh's age
Equation: 10 + t = ½(21 + t)
Multiply both sides by 2: 210 + 2t = 21 + t
Simplify: 210 + 2t - t = 21
210 + t = 21
t = 21 - 210
t = 21 - 20 = 1

At that time, Rakshit's age = 10 + 1 = 11
Verification: When Rakshit is 11, Santosh is 22 = 22
Check: Is 11 = ½ × 22? ½ × 22 = 11.0 ✓

Note: Mathematically, this always equals the age difference (11) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 14

When Ishwar was born, Cole was 9 years old. The sum of their present ages is 43. Find Ishwar's age when Ishwar was half of Cole's age (this will happen 8 years ago).

Let Ishwar's current age = 17, Cole's current age = 26
Given: When Ishwar was born (0 years old), Cole was 9 years old.
Therefore, Cole is always 9 years older than Ishwar.
So 26 = 17 + 9 ✓

Condition: Find t such that Ishwar's age = ½ of Cole's age
Equation: 17 + t = ½(26 + t)
Multiply both sides by 2: 217 + 2t = 26 + t
Simplify: 217 + 2t - t = 26
217 + t = 26
t = 26 - 217
t = 26 - 34 = -8

At that time, Ishwar's age = 17 + -8 = 9
Verification: When Ishwar is 9, Cole is 18 = 18
Check: Is 9 = ½ × 18? ½ × 18 = 9.0 ✓

Note: Mathematically, this always equals the age difference (9) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 15

When Upasana was born, Sheetal was 4 years old. The sum of their present ages is 18. Find Upasana's age when Upasana was half of Sheetal's age (this will happen 3 years ago).

Let Upasana's current age = 7, Sheetal's current age = 11
Given: When Upasana was born (0 years old), Sheetal was 4 years old.
Therefore, Sheetal is always 4 years older than Upasana.
So 11 = 7 + 4 ✓

Condition: Find t such that Upasana's age = ½ of Sheetal's age
Equation: 7 + t = ½(11 + t)
Multiply both sides by 2: 27 + 2t = 11 + t
Simplify: 27 + 2t - t = 11
27 + t = 11
t = 11 - 27
t = 11 - 14 = -3

At that time, Upasana's age = 7 + -3 = 4
Verification: When Upasana is 4, Sheetal is 8 = 8
Check: Is 4 = ½ × 8? ½ × 8 = 4.0 ✓

Note: Mathematically, this always equals the age difference (4) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 16

When Manjari was born, Willow was 3 years old. The sum of their present ages is 13. Find Manjari's age when Manjari was half of Willow's age (this will happen 2 years ago).

Let Manjari's current age = 5, Willow's current age = 8
Given: When Manjari was born (0 years old), Willow was 3 years old.
Therefore, Willow is always 3 years older than Manjari.
So 8 = 5 + 3 ✓

Condition: Find t such that Manjari's age = ½ of Willow's age
Equation: 5 + t = ½(8 + t)
Multiply both sides by 2: 25 + 2t = 8 + t
Simplify: 25 + 2t - t = 8
25 + t = 8
t = 8 - 25
t = 8 - 10 = -2

At that time, Manjari's age = 5 + -2 = 3
Verification: When Manjari is 3, Willow is 6 = 6
Check: Is 3 = ½ × 6? ½ × 6 = 3.0 ✓

Note: Mathematically, this always equals the age difference (3) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 17

When Uma was born, Falguni was 4 years old. The sum of their present ages is 20. Find Uma's age when Uma was half of Falguni's age (this will happen 4 years ago).

Let Uma's current age = 8, Falguni's current age = 12
Given: When Uma was born (0 years old), Falguni was 4 years old.
Therefore, Falguni is always 4 years older than Uma.
So 12 = 8 + 4 ✓

Condition: Find t such that Uma's age = ½ of Falguni's age
Equation: 8 + t = ½(12 + t)
Multiply both sides by 2: 28 + 2t = 12 + t
Simplify: 28 + 2t - t = 12
28 + t = 12
t = 12 - 28
t = 12 - 16 = -4

At that time, Uma's age = 8 + -4 = 4
Verification: When Uma is 4, Falguni is 8 = 8
Check: Is 4 = ½ × 8? ½ × 8 = 4.0 ✓

Note: Mathematically, this always equals the age difference (4) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 18

When Nicholas was born, Akshay was 4 years old. The sum of their present ages is 30. Find Nicholas's age when Nicholas was half of Akshay's age (this will happen 9 years ago).

Let Nicholas's current age = 13, Akshay's current age = 17
Given: When Nicholas was born (0 years old), Akshay was 4 years old.
Therefore, Akshay is always 4 years older than Nicholas.
So 17 = 13 + 4 ✓

Condition: Find t such that Nicholas's age = ½ of Akshay's age
Equation: 13 + t = ½(17 + t)
Multiply both sides by 2: 213 + 2t = 17 + t
Simplify: 213 + 2t - t = 17
213 + t = 17
t = 17 - 213
t = 17 - 26 = -9

At that time, Nicholas's age = 13 + -9 = 4
Verification: When Nicholas is 4, Akshay is 8 = 8
Check: Is 4 = ½ × 8? ½ × 8 = 4.0 ✓

Note: Mathematically, this always equals the age difference (4) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 19

When Disha was born, Mansi was 10 years old. The sum of their present ages is 60. Find Disha's age when Disha was half of Mansi's age (this will happen 15 years ago).

Let Disha's current age = 25, Mansi's current age = 35
Given: When Disha was born (0 years old), Mansi was 10 years old.
Therefore, Mansi is always 10 years older than Disha.
So 35 = 25 + 10 ✓

Condition: Find t such that Disha's age = ½ of Mansi's age
Equation: 25 + t = ½(35 + t)
Multiply both sides by 2: 225 + 2t = 35 + t
Simplify: 225 + 2t - t = 35
225 + t = 35
t = 35 - 225
t = 35 - 50 = -15

At that time, Disha's age = 25 + -15 = 10
Verification: When Disha is 10, Mansi is 20 = 20
Check: Is 10 = ½ × 20? ½ × 20 = 10.0 ✓

Note: Mathematically, this always equals the age difference (10) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 20

When Vaibhav was born, Brijesh was 21 years old. The sum of their present ages is 91. Find Vaibhav's age when Vaibhav was half of Brijesh's age (this will happen 14 years ago).

Let Vaibhav's current age = 35, Brijesh's current age = 56
Given: When Vaibhav was born (0 years old), Brijesh was 21 years old.
Therefore, Brijesh is always 21 years older than Vaibhav.
So 56 = 35 + 21 ✓

Condition: Find t such that Vaibhav's age = ½ of Brijesh's age
Equation: 35 + t = ½(56 + t)
Multiply both sides by 2: 235 + 2t = 56 + t
Simplify: 235 + 2t - t = 56
235 + t = 56
t = 56 - 235
t = 56 - 70 = -14

At that time, Vaibhav's age = 35 + -14 = 21
Verification: When Vaibhav is 21, Brijesh is 42 = 42
Check: Is 21 = ½ × 42? ½ × 42 = 21.0 ✓

Note: Mathematically, this always equals the age difference (21) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Master Age at Event - Intermediate-Advanced Level Problems Age at Event INTERMEDIATE ADVANCED

What you'll learn in this worksheet: